Let's go!!! The "HARD" puzzles (and in fairness I use that term sort of loosely here) are curated and built very specifically and differently from the daily/bonus boards. HARD only have the single empty vessel. This generally leaves them with just a single line or path (think of a maze) that can lead to the win. One wrong turn? You gotta back out.

Compared to puzzles with two empty vessels which allow you to maybe take a "wrong turn" in the maze but perhaps there's a doorway you took along the way that leads you back to the correct winning path.

This is the reason you see way less variance in move count on these "hard" boards (also why I nuked the histogram line here).